The effective conductivity of a periodic lattice of circular inclusions (Q2865458)

In this paper, the author studies the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. The goal is to find an analytic expression for the effective conductivity tensor. He reduces the problem to an infinite system of linear equations and finds its solution in the form of a convergent power series in terms of the volume fraction of the cylinders whose coefficients are determined explicitly. As a practice calculation, he gives the average electric field, the current density and the effective conductivity tensor that relates the two quantities for the effective conductivity tensor. The author reduces the problem to an infinite system of linear equations and finds its solution in the form of a convergent power series in terms of the volume fraction of the cylinders whose coefficients are determined explicitly.